(Solved): 5. a) Let \( P(x)=8-4(x-3)+5(x-3)^{2}-7(x-3)^{3}+9(x-3)^{4}-6(x-3)^{5} \) be the fifthdegree Taylo ...

5. a) Let \( P(x)=8-4(x-3)+5(x-3)^{2}-7(x-3)^{3}+9(x-3)^{4}-6(x-3)^{5} \) be the fifthdegree Taylor polynomial for the function \( f \) about \( x=3 \). Assume \( f \) has derivatives of all orders for all real numbers. Write the third-degree Taylor polynomial for \( f^{\prime} \) about \( x=3 \), and use it to write an unsimplified expression to approximate \( f^{\prime}(3.2) \).